
theorem
  3271 is prime
proof
  now
    3271 = 2*1635 + 1; hence not 2 divides 3271 by NAT_4:9;
    3271 = 3*1090 + 1; hence not 3 divides 3271 by NAT_4:9;
    3271 = 5*654 + 1; hence not 5 divides 3271 by NAT_4:9;
    3271 = 7*467 + 2; hence not 7 divides 3271 by NAT_4:9;
    3271 = 11*297 + 4; hence not 11 divides 3271 by NAT_4:9;
    3271 = 13*251 + 8; hence not 13 divides 3271 by NAT_4:9;
    3271 = 17*192 + 7; hence not 17 divides 3271 by NAT_4:9;
    3271 = 19*172 + 3; hence not 19 divides 3271 by NAT_4:9;
    3271 = 23*142 + 5; hence not 23 divides 3271 by NAT_4:9;
    3271 = 29*112 + 23; hence not 29 divides 3271 by NAT_4:9;
    3271 = 31*105 + 16; hence not 31 divides 3271 by NAT_4:9;
    3271 = 37*88 + 15; hence not 37 divides 3271 by NAT_4:9;
    3271 = 41*79 + 32; hence not 41 divides 3271 by NAT_4:9;
    3271 = 43*76 + 3; hence not 43 divides 3271 by NAT_4:9;
    3271 = 47*69 + 28; hence not 47 divides 3271 by NAT_4:9;
    3271 = 53*61 + 38; hence not 53 divides 3271 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3271 & n is prime
  holds not n divides 3271 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
